(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that [tex]\sum(-1)^n\frac{n}{p_n}[/tex] converges, where [tex]p_n[/tex] is the nth prime.

2. Relevant equations

The sequence [tex]\frac{n}{p_n}[/tex] is definately not monotone if there exists infinitely many twin primes, since [tex]2n-p_n<0[/tex] for sufficiently large n, so alternating series test is out. Are there any other ways of showing this converges?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Prove that the series SUM (-1)^n n/p_n converges where p_n are primes

**Physics Forums | Science Articles, Homework Help, Discussion**